SYMMETRY AND DEFECTS IN THE CM PHASE

OF POLYMERIC LIQUID CRYSTALS

Helmut R. Brand†$∗, P. E. Cladis‡ and Harald Pleiner†

FB 7, Physik, Universitat Essen, D 4300 Essen 1, F.R.G.AT&T Bell Laboratories, Murray Hill, NJ 07974, U.S.A.

Dept. of Electrical Engineering, KIT Tobata, Kitakyushu 804, Japan

Macromolecules 1992 25 p.7223-6

ABSTRACT: Motivated by the recent discovery of a novel biaxial and orthogonal

smectic polymeric liquid crystal with in-plane fluid order (smectic CM ), we discuss

defects allowed by its symmetry. Smectic CM has not yet be found in low molecular

weight liquid crystals. We point out that observation of defects provides a useful

tool to distinguish smectic CM from other biaxial and fluid smectic phases known

as smectics C and O. The structure of a possible ferroelectric, but non-chiral phase

(smectic CP ) is briefly discussed.

† University of Essen$ Kyushu Inst. of Technology‡ AT&T Bell Laboratories

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1. Introduction

Following the first synthesis in 1978 of liquid crystalline side-chain polymers,1 many

novel materials were synthesized with the electro-optical features of low molecular weight

liquid crystal materials combined with the structural properties of polymers.2,3 Most re-

cently, a fluid smectic phase that is biaxial and orthogonal has been reported for the first

time in ”side-on” liquid crystalline side-chain polymers and their mixtures with a low

molecular weight liquid crystal.4,5 In the side chain polymer exhibiting this novel phase,

the spacer group tethering a liquid crystal monomer to the polymer backbone is attached

to the monomer in a side-on connection much like an umbilical cord6. The understanding

is that this type of connection promotes the formation of biaxial liquid crystal phases by

reducing the monomer’s rotational freedom about its long axis.

The new biaxial, fluid and orthogonal smectic phase was found by cooling a ”side-on

side-chain liquid crystalline polymer,” called polymer 1, from a biaxial nematic state.5 It

was identified as biaxial from conoscopic observations in the polarizing microscope and

orthogonal and fluid in the layers from x-ray investigations.5. The new phase was found

to occur in mixtures of the polymer (containing a lateral naphthalene group in the side

chain; see refs. 4 and 5 for details) with a low molecular weight compound5 for mixtures

containing more than about 50% by weight of the polymer.

An intuitive picture is the following: when the fraction of board-like objects teth-

ered to the polymeric backbone in an umbilic fashion, and thus showing hindered rotation

about their long axis, becomes too small, the macroscopic biaxiality of the mixture goes to

zero leaving only uniaxial phases such as uniaxial nematics and smectic A. We note that

the parent polymer shows the phase transitions

g − 303K − CM − 319K −Nbx − 326K − i

and that the polymer and the low molecular weight material are miscible in all proportions5.

The width of the two phase regions ∆Tc in the mixtures with the low molecular weight

2

compound is ∆Tc ∼ 2K. For the complete phase diagram, we refer to Fig.5 of ref.5. Nbx

denotes a biaxial nematic phase and the label CM is explained below. This new phase has

all the properties of the smectic phase named smectic CM by de Gennes7 where M refers

to MacMillan who first described this phase.

Although a large number of smectic phases is known from studies of low molecular

weight systems, the smectic CM phase has so far only been identified for polymeric liquid

crystals.5 The most familiar7 low molecular weight smectic liquid crystal phases are the

ones showing fluidity in the layers such as smectic C. The possibility emerges that some

phases now classified as smectic C because they are fluid and optically biaxial, may turn

out to be actually smectic CM phases. Therefore, it is useful to give simple criteria based on

symmetry arguments to facilitate the identification of smectic phases, in particular smectic

CM , in polymeric and low molecular weight liquid crystals. The powerful link between

symmetry arguments and macroscopic physical properties of materials is illustrated by our

prediction of a novel ferroelectric fluid polymeric liquid crystal without chiral molecules in

another biaxial and fluid smectic phase.

In a mean field approximation,8 Brand and Pleiner discussed phase transitions in-

volving smectic CM and investigated the hydrodynamic and electrohydrodynamic proper-

ties of both smectic CM and smectic CM∗ , the chiralized version of smectic CM that has

a spiral structure but no tilt.9 In a mean field approximation, they find that the biaxial

nematic-smectic CM transition can be continuous.8 Indeed, DSC measurements4 in poly-

mer 1 show no evidence of a latent heat at the biaxial nematic-CM transition. Brand and

Pleiner also point out the possibility of continuous A−CM and CM -C phase transitions.8

So far, defects and their usefulness for identifying smectic CM liquid crystal phases

from macroscopic observations in the polarizing microscope of either polymeric or low

molecular weight liquid crystals have not been discussed. Indeed, as mentioned above, CM

may have already been observed but was not identified as such because it is a fluid biaxial

smectic phase similar to smectic C.

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A model for a new biaxial, orthogonal smectic phase, smectic CP , is shown in Fig.1.

In this model, the unit cell is a bilayer with orthorhombic symmetry, C2v: it lacks one

of the three possible mirror planes. As is well known10, bulk ferroelectricity is associated

with C2v symmetry with polarization, P (in Fig. 1) parallel to the two-fold axis. We note

that, such a structure is ferroelectric without chiral molecules (Fig.1).

At the other extreme, we point out that the biaxial orthogonal fluid smectic phase

observed in the non-chiral main chain liquid crystalline polymers BB5, BB7, BB9 etc.11,12

also has C2v symmetry, but antiferroelectric order. Both, the CP phase suggested here

and the phase found by Watanabe and Hayashi11,12 (that they call smectic C2), have a

chevron structure. One can easily imagine ferrielectric phases bridging the gap between

ferroelectricity and antiferroelectricity, that have also C2v symmetry.

Since smectic CP and smectic CM both have orthorhombic symmetry, they have the

same number of elastic constants and viscous coefficients even though x-ray measurements

show differences in their point symmetry.

Thus the discovery of CP would be the first time that a nonchiral material shows a

truly ferroelectric liquid crystal phase.

2. General Properties of Smectic CM

Here we point out that the knowledge of smectic CM defects and their properties

is useful for distinguishing between smectic A, nematics and, most importantly, from the

optically biaxial smectics C and CP phases. In particular, we suggest that differences in the

in-plane symmetry of the different smectic phases are most simply revealed by observations

of defects in the polarizing microscope of freely suspended films. In freely suspended

smectic films, defects in the layering are absent and the sample is most conveniently viewed

in a direction parallel to the layer normal. We stress that defects of the in-plane director

can also be obtained in bulk samples or in drops on free surfaces. In these cases, however,

it is more difficult to show, that one has only a defect in the in-plane director and not a

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combined defect in the layering and in the in-plane director. Because polymer dynamics is

slow relative to low molecular weight materials, these systems also present an opportunity

for studying e.g. coarsening dynamics and the associated scaling laws for topological

defects on experimentally accessible time scales.

Smectic CM has D2h, smectic CP , C2v and, the smectic C phase, C2h point (lo-

cal) symmetry. The usual nematic and smectic A liquid crystals, have uniaxial symmetry,

D∞h. Nematics have broken continuous rotational symmetry with a preferred direction,

characterized by a director, n, a unit vector, that does not distinguish between head and

tail.7 In smectic A, a layered state, the layer normal is a unit vector p that is indistin-

guishable from −p. In the plane of its layers, smectic A is an isotropic liquid7 and the

director n is parallel to p (see Fig. 1).

In classical smectic C phases, which are fluid and biaxial, the average direction of the

molecules, the director n, is at a constant tilt angle to the layer normal p. The projection

of n in the plane of the layers is called c. The smectic C ground state is invariant only

under the simultaneous replacements p → −p and c → −c. Because of the tilt, these

replacements cannot be made separately (see Fig. 1).

For an over-view of defects in liquid crystals other than smectic CM , see ref. 13.

Various textures are shown and explained in ref. 14.

In contrast to classical smectic C, smectic CM has no tilt and p ‖ n. The in-plane

preferred direction is characterized8 by a director, m, that is orthogonal to the layer normal

p. The ground state is invariant under the replacements p→ −p or m→ −m separately8

(see Fig. 1). As we will see in the following, this difference along with the higher local

symmetry of CM allows for a convenient qualitative optical distinction between smectic C

and smectic CM in freely suspended films.

As for smectic CP , the operation p → −p leaves the ground state invariant, an

operation equivalent to m → −m does not exist. This gives rise to the possibility for a

spontaneous polarization, P, in the plane of the layers for smectic CP (see Fig. 1).

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3. Defects of the in-plane director

First, we consider line defects in smectics associated with the in-plane director,

either m in CM or c in C when the smectic layers are flat: i.e. p is fixed. These defects,

called disclination lines or disclinations, are shown in Fig. 4.2 of ref. 7. On a circuit

around a disclination line, the director changes its ”inclination” (rotates) by 2πS where S

defines the strength of the line. For m→ −m symmetry, the lowest order defects are the

Mobius defects, S = ±1/2. In the absence of this symmetry, the lowest order defects are

S = ±1.

When viewed between crossed polarizers in a direction parallel to the defect line,

disclinations of strength S = ±12 are characterized by two black brushes while defects of

strength S = ±1 are characterized by four black brushes. Besides the number of brushes

radiating from a defect line, to identify defect strength it is also important to check the

rate of rotation of the brushes as the sample is turned between crossed polarizers. For

example, if the defect line is at an angle to the field of view, then, because of the more

complicated optics this implies, a defect of strength S = 1, could show two brushes and

not all four brushes normally associated with it. On the other hand, when a defect of

strength S = 1 is rotated between crossed polarizers, the four brushes do not move while

brushes associated with defects S 6= 1 are ”mobile”.

While defects of strength S = ±1 are equivalent to a defect free topology15 in

uniaxial nematics, this is not the case for biaxial nematics. This is because allowing a

singularity in n, say, to escape into the third dimension introduces a singularity in m in

biaxial nematics.

In smectic phases, there is a strong coupling between n and p so escape into the third

dimension introduces dislocations in the layered structure. Defects of strength S = ±1

in smectic systems have a singular core in contrast to defects of this strength in uniaxial

nematics. Thus, if no dislocations are introduced in the layering, disclination energies scale

like S2 making e.g. two S = 1/2 defects less energetic than one topologically equivalent

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S = 1 defect. But, an S = 1 will decay into two S = 1/2 defects if, and only if, S = ±1/2

disclinations are allowed by symmetry.

Because of the nematic-like m → −m equivalence in smectic CM , m can have

defects of strength S = ±12

and S = ±1, just as in uniaxial nematic liquid crystals. In

contrast to smectic CM , in the classical tilted smectic C phase, c is not equivalent to −c.

Therefore, only defects of strength S = ±1 (2π rotations) are possible for the in-plane

director, c, and no S = ±12 defects (π rotations) is allowed by its symmetry.16

This difference leads to the suggestion of how to distinguish smectic C and smectic

CM from the observations of defects in the polarizing microscope: if one observes that

a fluid, optically biaxial smectic phase has defects of strength S = ±12 , it cannot be a

classical smectic C phase, but possibly it will be a smectic CM phase with no tilt.

We point out that in the ferroelectric smectic CP phase introduced above, S = ±1/2

defects in the in-plane director are ruled out by symmetry, since the in-plane director in

CP as well as in C distinguishes head and tail.

We also note, that the C2 phase discussed above11,12 does not show S = ±1/2

defects, but rather dispirations, i.e. combined defects in the layering and the in-plane

director17,18. In contrast, smectic CM can show true S = ±1/2 disclinations without

additional defects in the layering. This is because smectic CM has D2h symmetry, while

the C2 phase of refs.13 and 14 has C2v symmetry. Thus, smectic CM is unique among

the fluid biaxial smectic phases in allowing for the existence of S = ±1/2 defects in the

in-plane director.

4. Defects Involving Layering and the In-plane Director

While the energy to compress or dilate layers is large, for layered systems with fluid

in-plane order, curvature energy to deform layers is small. The most famous defects for

smectic phases with in-plane fluidity are focal conic defects observed as singularities in

the layering along lines known as Dupin cyclides.7,19−21 When many occur, the resulting

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texture is known as a fan texture. The important property of focal conics is that they

conserve microscopic layer spacing when the layers are curved. Because layer curvature

energy is small, focal conic defects are easily observed with a polarizing light microscope

without special attention to sample preparation and become ”broken” when the layer

spacing changes as, for example, at a smectic A (unbroken fans) to C (broken fans) phase

transition. For the C phase, additional problems from tilt mismatch (see Fig. 25 of ref.

16) at focal conic line singularities provide another argument for why fan textures are

”broken” in the C phase but not in the A phase14.

Because of its m to −m symmetry, smectic CM does not have a matching problem.

Furthermore, the CM layer spacing, similar to smectic A, is close to the fully-extended

monomer length. On the basis of these two properties, we expect an unbroken fan tex-

ture for smectic CM , as is indeed observed.22 Thus, differences in fan texture provide a

qualitative macroscopic distinction between smectic C and CM .

Smectic phases with in-plane fluidity can also have edge and screw dislocations.19,20

For systems with in-plane anisotropy, layer defects may or may not be associated with

defects of the in-plane structure providing another way to distinguish between a CM phase

and A, CP or C phases.

For example, in an edge dislocation, the singular line (edge line) perpendicular to the

layer normal p can be decomposed21 into two half-integer (+1/2 and −1/2) disclinations

of the layer normal, p. In this description, that is all that can happen for smectic A

with p ‖ n. In a CM phase, whether m shows a defect or not depends on its orientation

relative to the edge line. If m is parallel to the edge line, there is no defect and m is

constant everywhere, while when m is perpendicular to the edge line, it makes a half-

integer disclination of the same sign as p. The latter type of edge dislocation is expected

to cost more energy, therefore, should occur less frequently than the first one.9

In smectic C, however, splitting an edge dislocation into two disclinations of the

layer normal, p, always has the geometrical implication of defects for the director n. c

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perpendicular to the edge line creates a disclination13 for n while c parallel to the edge line

creates an energetic tilt inversion wall14,16 for n where the tilt angle changes sign (see e.g.

Fig. 4 of ref.16). While tilt inversion defects may also play a role in the broken fan texture

observed when a smectic A phase transforms to a smectic C phase, being very energetic,

electron microscopy techniques are likely required to observe them.

Screw dislocations, where the singular line (the screw line) is parallel to the layer

normal p, are frequently seen in freeze fracture electron microscopy.20 In the A phase the

director is constant everywhere (except for some small core region that we disregard in

this discussion) and shows no defect. The same holds for a C phase and also for a CM

phase. As there is no qualitative difference for screw dislocations in these phases, they are

not expected to be useful for discriminating between smectic CM and smectics A or C.

5. Conclusions and Perspectives

Many compounds classified as smectic C solely on the basis of their in-plane fluidity

and optical biaxiality may turn out to be actually smectic CM or even CP phases. A

combination of the study of defects (presented here), of the phase transitions involving a

possible CM phase8 and, of the hydrodynamic and electrohydrodynamic properties9 will be

useful to find more examples of smectic CM and an example of CP in both polymeric and

low molecular weight liquid crystals. We have pointed out, that CM is unique among biaxial

smectic phases in that stable S = ±1/2 disclinations can occur without the introduction

of dislocations in the layer structure. This can be most conveniently and easily checked by

polarizing microscope observations. This method has been used by Takanishi et al.17,18 to

demonstrate that a dislocation always accompanies S = ±1/2 disclinations in the biaxial

orthogonal smectic phase found in the main chain polymer BB5.

The occurrence of the smectic CM phase seems much easier to achieve in a controlled

way, however, in side-on side-chain liquid crystalline polymers than in low molecular weight

materials or even in the more common end-on side-chain liquid crystalline polymers, where

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the mesogenic units are attached at one end of the mesogen to the spacer connecting to

the polymeric backbone. This feature can be traced back to the design of the side-on side-

chain liquid crystalline polymers: the molecules are attached to the polymeric backbone

in such a way as to prevent their rotation about their long axis thus giving rise only to

biaxial phases. In fact, this concept was pioneered by Hessel and Finkelmann6 in their

search for biaxial nematic phases in thermotropic liquid crystalline polymers. Therefore, it

appears completely natural that the smectic phase below a biaxial nematic phase in these

polymers is also biaxial and thus of the CM type and not of the usual uniaxial smectic A

type prevalent in end-on side-chain polymers and in low molecular weight materials. On

the basis of this reasoning we expect that the smectic CM phase will be most conveniently

obtained in side-on side-chain liquid crystalline polymers and, consequently, in sufficiently

concentrated mixtures with the more common end-on side-chain polymers or even low

molecular weight materials5.

After this analysis one might ask whether it is also possible to observe smectic CM

and its defects in main-chain liquid crystalline polymers in which the mesogenic units are

incorporated into the polymeric backbone. While a CM phase has not yet been reported,

perhaps partly because one has not applied the concept outlined above for side-chain poly-

mers to main-chain polymers, it seems worthwhile to notice, that already in 1988 Watanabe

and Hayashi11,12 discussed, on the basis of their x-ray analysis, a fluid orthorhombic biaxial

phase. They suggested that the occurrence of such a phase is favored over smectic A and

C in the odd homologues of the BBn series11,12 by packing arguments. In this case the

picture is that molecules in one layer tilt in one direction and in the next layer they tilt

in the opposite direction thus giving rise to a chevron structure, that is orthorhombic, i.e.

a fluid biaxial smectic phase. The resulting overall symmetry is, however, not D2h as for

smectic CM , but rather C2v. We point out here that the model presented by Watanabe

and Hayashi11,12 implies antiferroelectricity in the nonchiral compound, a suggestion that

should surely be checked experimentally by looking at a P −E - loop on a sample of this

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compound.

We note, that the study of defects and their motion, for example in an external

electric field, has become of interest recently also outside the field of liquid crystalline

polymers, namely in block copolymers23, where one has observed defects that are similar

to those observed in smectic liquid crystalline polymers.

In the present paper, we have presented general symmetry arguments that apply to

low molecular weight liquid crystals as well as they do to polymeric liquid crystals. Hessel

and Finkelmann6 have shown that the polymeric structure can be used to control the

rotations of the mesogenic units leading to novel ordered structures that are more difficult

to obtain in non-polymeric materials. For example, we pointed out here, for the first time,

the possibility of a side-on side chain liquid crystalline polymer that is ferroelectric in the

bulk without chiral molecules. Development of such a material would open the door for

new optoelectronic applications that will emerge when ferroelectricity in a liquid crystalline

material is coupled with the structural advantages provided by polymers.

Acknowledgement. It is a pleasure for HRB and PEC to thank Heino Finkelmann for

stimulating discussions.

Support of this work by the Deutsche Forschungsgemeinschaft (HRB and HP) and by

NATO CRG 890777 (PEC and HRB) is gratefully acknowledged. HRB thanks Kyushu

Institute of Technology for the award of the KIT fellowship 1991.

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Figure Caption

Fig. 1: Structure of smectics A, C, CP and CM .

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References and Notes

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(22) Finkelmann, H., private communication.

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